The long-term performance of orthopedic implants depends crucially on a close match between the mechanical behavior of bone and of the implant material. Yet, the present man-made materials with the required biocompatibility and strength are substantially stiffer than bone. This mismatch results in stress shielding, which can lead to the loss of bone mass and may even lead to a revision surgery. Here we report a new materials design strategy towards metal-polymer composites that are based on constituents with established biocompatibility and that can be matched to bone. Ti-based nanoporous alloys, prepared by liquid-metal dealloying, are infiltrated with epoxy to form interpenetrating-phase nanocomposites. At up to 260 MPa, their yield strength is technologically interesting for a deformable light-weight material. More importantly, Young's modulus can be adjusted between 4.4 and 24 GPa, which affords matching to bone. As another parallel to bone, the strength of the composite materials is strain-rate dependent. These findings suggest that the novel composite materials may provide the basis for promising future implant materials.